I did a search and could not find anything related, I apologize if I wasn't able to locate an already discussed topic. Just wondering what airlines everyone has flown that are no longer around these days (out of business, merged, other)?

Ansett New Zealand/Qantas New Zealand
Sky Europe
BMI British Midland (not sure whether it counts since BA acquired it before it could completely collapse)
CP ( Not quite sure whether this counts since it was absorbed by AC before it could completely collapse)

Memories
Air UK for excellent catering, the best economy food I ever received
Go - first experience of a LCC
Brittania, great service for a charter airline.
Carib - scheduled inter island flight on an Islander.

Flying Colours (first flight on one of their 757-200s out of Bristol to Palma rt in 1999)
Air 2000 (the year after, first flight on an A321 again Bristol-Palma rt)
Not sure if this counts but whatever the BA regional (pre-flyBE) was with Dash 8s. Southampton-Manchester rt (2001/2002?)

I can recall only one offhand; Indonesia's Sempati Air which went bankrupt in 1998 following the Asian financial Crisis.
For the best part of the 1990s, I usually did my frequent SIN-JKT-SIN runs on this then President Suharto family/cronies' airline. It was my carrier of choice for two primary reasons: easier passage through immigration/customs and their mainly "on-time arrival" at destination airport.
Their almost perfect "punctuality" was due to their insanely long block time; about half an hour longer than all other airlines on the SIN-JKT-SIN route. In fact, my dozens of flights with them mostly landed before the ETA. Rarely did I arrive later and that only by not more than 15 minutes. I actually do wish I can exceed by over 30 minutes of their ETA because of their guarantee of a free flight. No such luck for me as the 30 minutes guarantee plus their safety margin of another half an hour made it very safe for them to keep to their "never later than half an hour late" pledge.

Ah, also ValuAir which is basically defunct except in name. After operating for barely more than a year, it was acquired by Jetstar in mid 2005. That it still "exists" is because Jetstar is using its permit to operate to Indonesia. Other than that, it is effectively Jetstar now; their grand fleet of two A320s painted in Jetstar colors with the Valuair logo displayed next to it to keep up the myth of still being around.

Pan Am in the 60's & 70's
Eastern in the 60's
Canadian Pacific in the early 70's
TAA in the 70's & early 80's
Ansett in the 70's, 80's and 90's
Australian Airlines in the early 80's
Compass Airline in the late 80's
Continental in the mid 80's
Lauda Air in the late 90's
Ted in the mid 2000's

TWA and Northwest, both while traveling from Seattle to the Midwest. I guess another one would be AirOne, which was Taquan Air's FAR 121 operation. Flew them on a couple flights from JNU-KTN (I think KTN, maybe Klawock as well).